Enrico's explanation is mostly correct: the image resolution as pixels/inch is arbitrary and has nothing to do with optical magnification.

But it is not just a "legacy" setting. If you want to insert text or to make measurements in inches using Photoshop's ruler, then you must have an appropriate pixels/inch value. 12 point text at 300 pixels per inch will cover many more pixels than 12 point text at 72 pixels per inch!

All Ex wrote:

photoshop is telling that the width of that image is 7360 pixels when the resolution is 300 pixels/inch, can you please tell me the logic behind that estimation?

Pixels divided by inches = pixels/inch.

Photoshop is telling you that the nominal print size is currently set to 24.533 inches. 7360 pixels divided by 24.533 inches = 300 pixels/inch.

If you went to Image > Image Size, removed the checkmark on "Resample", and changed the Width to be 10.5 inches, then you would see that the pixels/inch number would change to be about 700.95, because 7360/10.5 = 700.95 .

Quote:

That Rik`s calculation just got me very curious. Besides all the literature it was very accurate.

Can you explain in more detail: what about my calculation makes you curious?

When you are able to calculate the width in pixels (which after all are arbitrary, relating to the resolution). The removal of the checkmark is the key there and the right way to calculate the size of them, in fact, I`ve got confused in my habit to think with centimeters, after all, the scale in the measurement of the width of the frame is in mm and that got me more into thinking in that way._________________All--Ex
My YouTube initial video

I`ve got confused in my habit to think with centimeters, after all, the scale in the measurement of the width of the frame is in mm and that got me more into thinking in that way.

When you are clear on the concepts, the Photoshop ruler can also be used to make measurements directly, without counting pixels.

Here I have used Image Size to declare that the width of the image is 36 mm, equal to the sensor size.

Then I use the ruler to measure the distance between two lines that I know are 6 mm apart on the subject.

Photoshop says that the distance is 32.1 mm, and because I set the image size to be the same width as the sensor, I know that this is also 32.1 mm on the sensor.

Then 32.1 mm on sensor, divided by 6 mm on subject, gives an optical magnification of 32.1/6 = 5.35X . This is the same value, to within available precision, as the 5.338X that I got earlier by counting pixels. That's just as it should be, because under the covers all that's happening is that Photoshop is counting pixels and doing part of the calculation for me.

Quote:

To be super accurate you'd need a flat, aligned subject all in focus

This is certainly true, for some definition of "super accurate".

But it turns out that
1) the center of a line can be accurately estimated even if the edges of the line are blurred, and
2) the error due to having the target tilted with respect to the optical axis is only a factor of 1-cosine(theta), which even at 8 degrees gives less than 1% error. For smaller tilts the error is proportional to tilt squared. 5 degrees tilt gives only 0.38% error.

The combined effect of these two facts is that accurate measurements can be made even from pretty casual calibration shots, such as the one presented by All Ex.

In this whole debugging exercise, I guess the key thing was to actually see the calibration image, instead of trusting that somebody else has done the right thing with it. Earlier, when I asked All Ex how he had made the measurement, he replied that "magnification = sensor width/ frame width I use for the calculation of the frame width a ruler which has lines every half of a mm". Those words did not indicate any problem, but I now understand (I think!) that through confusion he was getting the wrong frame width to plug into the calculation.

but I now understand (I think!) that through confusion he was getting the wrong frame width to plug into the calculation.

To admit the truth it was a childish mistake of mine. I apologize to all of you, I am truly feeling very embarrassed for my mistake, and I can`t think how I did that.
I was calculating the hight instead of the width of the frame (24mm instead of 36mm), I can`t think how I did that.
Though this discussion was very helpful, through it I understood many thinks, firstly now I am rearranging the measurement units in my photoshop which in some other time mess it, resulting not to have these measurements that appear in the last Rik`s post.
Once again I apologize to all of you.
_________________All--Ex
My YouTube initial video

After I realized what I have done I`m living for the rest of the day in depression. I`m almost 50 and this is a mistake hard to accept. It doesn`t escape my mind. This kind of photography has become for me an obsession.
Your explanation in that estimation is certainly one of the positive things in that thread, together with the tube lens of course.
Anyway, thank you for your interest, and your kind words._________________All--Ex
My YouTube initial video